[gpaw-users] Generating new basis sets for LCAO mode

[Eric Hermes]

Hello,

I have a couple of questions regarding how GPAW basis sets for LCAO mode 
are generated, specifically with regards to platinum.

First, I would like to point out what I think is a problem with the 
basis sets that are packaged with the most recent setups tarball. For 
the DZP basis set, all of the D-block metals have either D-like or 
P-like polarization functions instead of F-like.  This is different from 
the DZP basis sets generated by using all default parameters with 
gpaw-basis (version 0.9.1.10133), which does generate F-like 
polarization functions.  I mentioned this in the IRC channel, and Ask 
agreed that the basis sets in the setups tarball are wrong.

Moreover, I am somewhat confused as to why some of the polarization 
functions in the basis sets that I generate with my gpaw-basis are 
P-like (Co, Cu, and Au are all P-like, whereas Ni, Rh, Pd, Ag, Ir, and 
Pt are all F-like).  From a physical standpoint, it seems to me that a 
polarization function for any element with D valence orbitals should 
have F-like polarization functions.  It is not clear to me what the 
physical interpretation of a P-like polarization function would be given 
that an orbital can only really be polarized by a function that has less 
symmetry.

The --help information for gpaw-basis says that the default behavior for 
generating polarization functions is to assign it the lowest l which is 
not among the valence states.  This ties into my second question, as it 
turns out that gpaw-basis is doing exactly what it says. Co, Cu, and Au 
do not include their largest occupied P orbitals in their valence count, 
whereas the other elements I have listed do.  This means that Co has 9 
electrons in its valence whereas Rh and Ir both have 15, and Cu and Au 
have 11 electrons in their valence whereas Ag has 17.  Is there some 
reason for this difference?  Even though these elements do not have P 
orbitals in their valence, does it not still make sense to use F-like 
polarization functions?  Also, is it possible to generate a new setup 
and basis for platinum along the lines of Co, Cu, and Au such that it 
only has 10 electrons in its valence which is composed of the 6S and 5D 
orbitals?

I have also been trying to figure out how to generate a basis for Pt 
that includes its empty 6P orbital, following the guide on the wiki 
(https://wiki.fysik.dtu.dk/gpaw/documentation/lcao/lcao.html#advanced-basis-generation). 
I have only just now figured out how do to this, as the page linked has 
a typo (should be jvalues instead of lvalues).  I also found this syntax 
to be fairly confusing, and it is still not clear to me how to parse the 
argument that jvalues accepts.  Specifically, why is it a list rather 
than an integer indicating how many valence orbitals to include?

Finally, I am curious as to how valence atomic orbitals are generated 
for e.g. double-zeta and triple-zeta basis sets.  I noticed when playing 
around with generating basis sets for Pt that all primitives in the dzp 
basis are included in the tzp basis, and that the only addition were a 
set of tighter primitives.  It is my understanding that when increasing 
the number of primitives in GTOs such as going from 6-31G to 6-311G, the 
larger basis set is typically more diffuse in character.  Is there any 
particular reason that the basis sets for GPAW add tighter functions 
rather than more diffuse functions with increasing zeta?

Thanks for helping me understand the way GPAW handles LCAO and basis 
sets, and I apologize for the overly long email.

Eric Hermes